Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

<image>

You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 200000;
const int INF = 1e9 + 5;
int sy, a, b, N, Q, sum[MAXN + 5];
vector<pair<int, pair<int, int>>> segs;
bool cmp(const pair<int, pair<int, int>> &p, double x) { return p.first < x; }
double calc(double x) {
  auto it = lower_bound(segs.begin(), segs.end(), x, cmp);
  if (it == segs.end()) return sum[N];
  int l = it->second.first, r = it->first, idx = it->second.second - 1;
  return max(0.0, x - l) + sum[idx];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> sy >> a >> b >> N;
  for (int i = 1; i <= N; i++) {
    int l, r;
    cin >> l >> r;
    segs.push_back({r, {l, i}});
    sum[i] = sum[i - 1] + r - l;
  }
  cin >> Q;
  for (int q = 0; q < Q; q++) {
    int x, y;
    cin >> x >> y;
    double i1 = x + (double)(x - a) / (y - sy) * -y,
           i2 = x + (double)(x - b) / (y - sy) * -y;
    cout << fixed << setprecision(10) << (calc(i2) - calc(i1)) * (y - sy) / y
         << "\n";
  }
}